Well-Posedness of Mild Solutions for Superdiffusion Equations with Spatial Nonlocal Operators

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-02 DOI:10.1007/s12346-024-01084-y

Xuan-Xuan Xi, Yong Zhou, Mimi Hou

引用次数: 0

Abstract

In this paper, we study the well-posedness for a class of semilinear superdiffusion equations with spatial nonlocal operators. We first establish the Gagliardo–Nirenberg inequality in \(\psi \)-Bessel potential spaces. Based on this, the well-posedness results of local and global mild solution for corresponding linear problem are obtained via apriori estimates. We also obtain the well-posedness results for the nonlinear problem under different conditions. These conclusions are mainly based on the Mihlin–Hörmander’s multiplier estimates, embedding theorem and fixed point theory.

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带空间非局部算子的超扩散方程温和解的良好拟合

本文研究了一类带有空间非局部算子的半线性超扩散方程的好拟性。我们首先建立了贝塞尔势空间中的 Gagliardo-Nirenberg 不等式。在此基础上，通过先验估计得到了相应线性问题的局部和全局温和解的拟合结果。我们还得到了非线性问题在不同条件下的良好求解结果。这些结论主要基于 Mihlin-Hörmander 乘数估计、嵌入定理和定点理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.